# Properties

 Label 87120.bn Number of curves $6$ Conductor $87120$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bn1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.bn1 87120t4 $$[0, 0, 0, -57499563, -167820468662]$$ $$15897679904620804/2475$$ $$3273096420633600$$ $$[2]$$ $$3932160$$ $$2.8236$$
87120.bn2 87120t6 $$[0, 0, 0, -30492363, 63566853658]$$ $$1185450336504002/26043266205$$ $$68882522341166464296960$$ $$[2]$$ $$7864320$$ $$3.1702$$
87120.bn3 87120t3 $$[0, 0, 0, -4138563, -1774758062]$$ $$5927735656804/2401490025$$ $$3175882183844361446400$$ $$[2, 2]$$ $$3932160$$ $$2.8236$$
87120.bn4 87120t2 $$[0, 0, 0, -3594063, -2621673362]$$ $$15529488955216/6125625$$ $$2025228410267040000$$ $$[2, 2]$$ $$1966080$$ $$2.4771$$
87120.bn5 87120t1 $$[0, 0, 0, -190938, -53675237]$$ $$-37256083456/38671875$$ $$-799095805818750000$$ $$[2]$$ $$983040$$ $$2.1305$$ $$\Gamma_0(N)$$-optimal
87120.bn6 87120t5 $$[0, 0, 0, 13503237, -12913790582]$$ $$102949393183198/86815346805$$ $$-229620202734149609564160$$ $$[2]$$ $$7864320$$ $$3.1702$$

## Rank

sage: E.rank()

The elliptic curves in class 87120.bn have rank $$1$$.

## Complex multiplication

The elliptic curves in class 87120.bn do not have complex multiplication.

## Modular form 87120.2.a.bn

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.